Non-LTE effects for Na I lines in X-ray illuminated stellar atmospheres

The formation of Na I lines in X-ray illuminated atmospheres is investigated by abandoning the assumption of local thermodynamic equilibrium (LTE). Calculations are performed on the basis of a 21-level Na I model atom for the LTE model atmospheres of irradiated F-G stars obtained with allowance for a reflection effect in the first approximation. The state of extreme “overrecombination” is shown to exist for the populations of all Na I levels in the case of external illumination. Absorption features in the profiles of “cool” and “normal” Na I lines have been found to be enhanced compared to the LTE approximation. Effects of the angle of incidence and intensity of the external radiation on the formation of level populations and line profiles when abandoning LTE are analyzed. The existence of overrecombination for Na I is explained by the small X-ray heating function and the large optical cooling function. Na I level populations are shown to depend weakly on the presence of “overionization” for Na II in the atmospheres of irradiated stars.     

Diagnostics for regions of formation of atomic lines in stellar atmospheres

We present a procedure to make direct diagnostics of the physical conditions of the regions of formation of the atomic spectral lines in stellar atmospheres using the atomic line widths at half maximum and the number of lines visible of a given atomic series in the observed stellar spectra. This is accomplished using the theoretical widths at half maximum of the atomic lines induced by the broadening produced by thermal energy fluctuations and considering the maximum number of levels that exist in those atoms under the physical conditions of the given system. The procedure is easy to use in any application. As an example we apply the procedure to the observed Lyman lines of hydrogen in the ultraviolet of some stars.     

Helium in stellar atmospheres

Helium, which was first discovered on the sun with the help of spectral analysis, plays, together with hydrogen, a principal role in astrophysics. We consider here two fundamental quantities: primordial helium abundance formed during Big Bang nucleosynthesis and the current initial helium abundances in nearby stars. It is shown that stellar atmospheres are enriched in helium during the main-sequence stage. Observational evidence for helium contamination in close OB-binaries is discussed. Stars with strong abundance anomalies are considered, such as chemically peculiar Ap and Bp helium-deficient stars and some types of objects with helium atmospheres.     

The transfer of polarized radiation in spectral lines: Solar-type stellar atmospheres

The polarization structure in several spectral lines in solar type stars is computed using the method described by McKenna (1981, 1984a). The frequency redistribution function used for these calculations is a linear combination ofR _II andR _III. The line profiles and polarization structures have been computed for several weak solar resonance lines includingKi 7664 Å, Sri 4607 Å, Baii 4554 Å, for various polar angles along the stellar disk. Both the line profiles and polarization structures as well as the center to limb behavior of the line center polarization agree well with observations.The somewhat stronger resonance line Cai 4227 Å shows a different polarization structure when compared to the weaker solar resonance lines. It is found that for strong resonance lines the proper redistribution function to be used is a linear combination ofR _III andR _v (see McKenna, 1981, 1984b; Heinzel, 1981). The major reason for this is that for strong resonance lines both the upper and lower levels are broadened by collisions. This violates the assumptions upon which the redistribution functionsR _II andR _III are based.     

Formation of spectral lines in stellar atmospheres. Linear and nonlinear theory

The present paper represents a short review of some directions of radiative transfer theory in spectral lines (RTSL) concerning investigations of authors in this field.Published in Astrofizika, Vol. 38, No. 4, pp. 565–571, October–December, 1995.     

Convective energy transport in stellar atmospheres

We discuss a theoretical method of computing the temperature structure of hot and cool streams in convective stellar atmospheres. The method is based on the model that the streams are due to organized cells whose diameters are greater than the thickness of the photosphere. The excess thermal energy of matter rising from the deeper layers, where the entropy is higher than in the photosphere, is converted to radiation in a steady front. This model, applied to the solar case, exhibits a peak-to-peak contrast of 30–40% between granules and lanes. This contrast agrees with the Stratoscope data reduced by Namba and Diemel (1969). As a necessary part of the theory, we obtain an expression for the perturbation in radiative heat exchange which may be used in a medium with a strongly preferred direction such as a stellar atmosphere.Supported in part by the National Science Foundation [GP-15911 (formerly GP-9433), GP-9114] and the Office of Naval Research [Nonr-220(47)].     

Convective energy transport in stellar atmospheres

The motion of convective cells in an environment which changes rapidly with depth is examined. In such an environment a cell may move through regions with different levels of ionization and with associated differences in heat capacity. The energy equation is cast in a manner which is independent of the history of these cells. The convective flux at a given level of the atmosphere is written as an average over an ensemble of cells originating at a range of other levels. A procedure for correcting the temperature gradient for these non-local effects is described and results for a model solar atmosphere are given. The principal results are: (1) The rms velocity varies smoothly and is non-zero well into the photosphere (e.g.,v _rsm=1.4 km/sec at =0.2); (2) Convective overshoot reduces the radiative flux to 60% and 90% of the total at =2.5 and 0.2 respectively; and (3) The interior adiabat of the convective envelope is less sensitive to the assumed value of the average cell size than in the usual treatment of convection.Supported in part by the National Science Foundation [GP-9433, GP-9114], the Office of Naval Research [Nonr-220(47)], and Air Force Grant AG-AFOSR-171-67.     

Formation of Zr I and II lines under non-LTE conditions of stellar atmospheres

The formation of Zr I and Zr II lines in stellar atmospheres under non-LTE conditions has been considered for the first time. A model zirconium atom has been composed using 148 Zr I levels, 772 Zr II levels, and the ground Zr III state. Non-LTE calculations have been performed for model atmospheres with T _eff = 5500 and 6000 K, log g = 2.0 and 4.0, [M/H] = −3, −2, −1, 0. In the entire investigated range of parameters, the Zr I levels are shown to be underpopulated relative to their LTE populations in the line formation region. In contrast, the excited Zr II levels are overpopulated, while the ground state and lower excited levels of Zr II retain their LTE populations. Since the non-LTE effects cause the Zr I and Zr II spectral lines being investigated to weaken, the non-LTE corrections to the abundance derived from Zr I and Zr II lines are positive. For Zr II lines, they increase with decreasing metallicity and surface gravity up to 0.34 dex for the model with T _eff = 5500, log g = 2.0, and [M/H] = −2. The non-LTE effects depend weakly on temperature. The non-LTE corrections for Zr I lines reach 0.33 dex for solar-metallicity models. Zr I and Zr II lines in the solar spectrum have been analyzed. The non-LTE zirconium abundances derived from lines in the two ionization stages are shown to agree between themselves within the error limits, while the LTE abundance difference is 0.28 dex. The zirconium abundance in the solar atmosphere (averaged over Zr I and Zr II lines) is log ɛ_Zr,⊙ = 2.63 ± 0.07.     

Turbulence influenced line formation in stellar atmospheres

The influence of stochastic velocity fields with finite correlation lengths on the formation of spectral lines is taken into account without restrictions to specific velocity models. To construct a perturbation theory treating the influence of stochastic motion on the radiative transfer we start with the stochastic transfer equation for plane-parallel atmospheres and expand it to an infinite hierarchical system. An appropriate cut-off of the infinite system admits to achieve exactly the micro- and macroturbulent limit at every level of approach. The formalism is derived for n-point correlations of the absorption coefficient and specialised for 2-point correlations.     

A graphical method for estimating overshoot in convective stellar atmospheres

A graphical method for estimating convective overshoot in stellar atmospheres is proposed. Applying the method to the solar atmosphere, we find that a convective element which starts at a depth of about 1000 km below the top of convection zone can penetrate to a height about 300 km above it.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

Pinchrosphere — The coolest layer in stellar atmospheres

An attempt is made to demonstrate the possibility of the existence of one more layer—pinchrosphere—in the structure of atmospheres of late-type stars—later than G5. Pinchrosphere is the coolest layer with very low electron temperature, 5500K, it is located on the photosphere and near the inner boundary of the chromosphere. Practically all elements in pinchrosphere, particularly hydrogen and magnesium, are in neutral state. The main physical parameters of the pinchrosphere are derived.     

The Rosseland mean opacity of stellar atmospheres

Rosseland mean opacities $\text{a}\text{?}{}_{\mathrm{R}}\text{(T,}\text{lgP}{}_{\mathrm{e}}\text{)}$ [see Table 2] per unit hydrogen particle are calculated in this paper for the atmosphere of the solar type [see Table 1].The sources of the continuous opacities under consideration in this paper are as follows: (1) H^?, HI, H^?₂, H⁺₂ He^?, HeI, HeII, CI, CII, CIII, NI, NII, NIII, OI, OII, NaI, MgI, MgII, AlI, AlII, SiI, SiII, CII, KI, CaII in the form of absorption. (2) HI, HeI, CI, NI, OI, H₂ in the form of Rayleigh scattering. (3) Free electrons in the form of Thomson scattering.     

On the influence of density and temperature fluctuations on the formation of spectral lines in stellar atmospheres

A method taking into account the influence of temperature and density flucuations generated by the velocity field in stellar atmospheres on the formation of spectral lines is presented. The influenced line profile is derived by exchanging the values in a static atmosphere by a mean value and a fluctuating one. The correlations are calculated with the help of the well-know hydrodynamic eqs. It results, that in normal stellar atmospheres the visual lines are only very weakly influenced by such fluctuations due to the small values of the gradients of the pressure and density and of the velocity dispersion.     

A relaxation method for the computation of model stellar atmospheres

A general Monte Carlo relaxation method has been formulated for the computation of physically self-consistent model stellar atmospheres. The local physical state is obtained by solving simultaneously the equations of statistical equilibrium for the atomic and ionic level populations, the kinetic energy balance equation for the electron gas to obtain the electron temperature, and the equation of radiative transfer. Anisotropic Thomson scattering is included in the equation of transfer and radiation pressure effects are included in the hydrostatic equation. The constraints of hydrostatic and radiative equilibrium are enforced. Local thermodynamic equilibrium (L.T.E.) is assumed as a boundary condition deep in the atmosphere. Elsewhere in the atmosphere L.T.E. is not assumed.The statistical equilibrium equations are solved with no assumptions made concerning detailed balance for the bound-bound radiative processes. The source function is formulated in microscopic detail. All atomic processes contributing to the absorption and emission of radiation are included. The kinetic energy balance equation for the electron gas is formulated in detail. All atomic processes by which kinetic energy is gained and lost by the electron gas are included.The method has been applied to the computation of a model atmosphere for a pure hydrogen early-type star. An idealized model of the hydrogen atom with five bound levels and the continuum was adopted. The results of the trial calculation are discussed with reference to stability, accuracy, and convergence of the solution.Contribution No. 385 from the Kitt Peak National Observatory.Operated by the Association of Universities for Research in Astronomy, Inc., under contract with the National Science Foundation.     

Magnetodynamic phenomena in the solar and stellar outer atmospheres

Magnetic effects causing anomalous heating and drastic flarings in the atmospheres of various types of stars are discussed. The best studied examples of these magnetic effects with spatially resolved observations are those in the case of the Sun, but no simple application of the solar knowledge to the stellar cases is allowed, since there are generally very large differences in the physical conditions between the Sun and other types of stars. We examine possible effects of the magnetic field in the respective situations of several types of stars which show X-ray and radio emissions indicating the presence of such activities, and it is concluded that the magnetic field may be playing important roles in producing anomalous heating and drastic flarings also in those stars having very different physical conditions, in ways seemingly very different from, but intrinsically closely related to, those in the case of the Sun.Invited review paper presented at the IAU Third Asian-Pacific Regional Meeting, held in Kyoto, Japan, between 30 September–6 October, 1984.     

Curvature effects in extended stellar atmospheres — Pure absorption

The effects of curvature in an atmosphere with pure absorption are investigated. Numerical solution of the transfer equation has been obtained in the framework of the Discrete Space Theory of Radiative Transfer. Two cases have been considered: (a) the atmosphere is irradiated at the bottom and there is no incident radiation at the top of the atmosphere; and (b) no radiation is incident on either side of the atmosphere. It is found that the thermal sources inside the atmosphere dominantly influence the emergent radiation and this is very much so, in the spherical case and for large optical thickness. The emergent luminosities increase with the geometrical thickness although the emergent specific intensities are reduced and the former seems to be because of the larger surface area and later seems to be because of the effects of curvature.     

Simple distribution functions for stellar systems

We use two elementary solutions of the integral equation connecting the density of a stellar system with its two-integral distribution function in order to construct simple distribution functions. Applications for axisymmetric, disk-like and spherical systems are given.     

On convection in stellar atmospheres far from local thermodynamic equilibrium

Non-thermal effects generated by sub-photospheric convection are considered. It is shown that convective cells are destroyed by shocks generated when convective velocities reach the speed of sound. Terminologically this process is given the name of sonic-boom-interrupted convection. An estimate is made on the dependence of convective velocities on stellar parameters. It is suggested that the process being investigated could explain why some stars do not belong to any branch of the theoretical Hertzsprung-Russell diagram.